Stochastic H2/H∞H2/H∞ control with (x,u,v)(x,u,v)-dependent noise: Finite horizon case

In this paper, the finite horizon mixed H2/H∞H2/H∞ control problem is studied for the systems governed by Itô-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed H2/H∞H2/H∞ control under consideration is associated with the four cross-coupled Hamilton–Jacobi equations. A discrete approximation algorithm is presented for solving the coupled generalized differential Riccati equations arising from linear stochastic H2/H∞H2/H∞ control. A necessary condition and a sufficient condition for the existence of the finite horizon stochastic H2/H∞H2/H∞ control are derived. In particular, some previous results on deterministic and stochastic H2/H∞H2/H∞ control can be viewed as corollaries of our main theorems.